An evening stroll through the Public Garden this week revealed miniature Easter bonnets sitting undisturbed on the sculpted heads of Mrs. Mallard and her eight bronze ducklings. In the nearby Boston Common, a bunch of inebriates were disturbing the peace near the Soldiers and Sailors Monument. That pretty much sums up the difference between the Garden and the Common — Boston’s notable downtown parks.

Regardless of intermittent efforts to dress it up, the Boston Common gets insufficient attention from the Boston Parks and Recreation Department. At its annual meeting on Tuesday, the nonprofit Friends of the Public Garden released its strategic plan warning that the Common can’t thrive under its current maintenance program. Elizabeth Vizza, the executive director of the Friends, cited “a huge imbalance between use and care’’ at the Common. Much of that use is due to positive developments like the big bump in residents and students living in nearby Downtown Crossing. But the combination of new users and 700 annual events doesn’t allow the turf much time to rest. The place is looking unusually shabby.

At 48 acres, the Common can accommodate nearly everyone from homeless people to office workers. But a recent rash of random assaults in and around the Common should be seen as a sign of underlying disorder, not a sign of spring. The “broken windows theory’’ of urban decay applies to parks as well as buildings. When a park starts to run down, aggressive panhandlers and drug dealers move in like invasive species. In addition to better maintenance, the Common needs more attention from police and park rangers pretty much around the clock.

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The well-heeled Friends group cares for 1,700 trees and more than 40 pieces of public art throughout the Public Garden, Boston Common, and Commonwealth Mall. The group is often accused of lavishing attention on the Garden at the expense of the Common. If that were ever the case, it’s not any longer. This year, the Friends completed a campaign to raise $4 million to restore and maintain the plaza and adjoining parkland near the Brewer Fountain at the busy southeast corner of the Common.

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Despite active Friends groups citywide, Boston’s roughly 200 parks and playgrounds have inched slowly downhill since 2000, when the Trust for Public Land cited the system for “unending creativity.’’ The late Justine Liff, who served as parks commissioner from 1996 until her death in 2002, was both a visionary and a brilliant fund-raiser. Custodial leadership and flat budgets would best characterize subsequent years. Only by folding in the costs of running city-owned cemeteries, for example, does the Parks and Recreation budget approach 1 percent of total city expenditures.

Newly elected Mayor Martin Walsh has expressed strong commitment to the city’s park system as recently as this week when he released a pair of swans — Romeo and Juliet — into the Public Garden lagoon. But there is nothing in his first operating budget to suggest that parks will be an especially high priority. In February, he appointed former arts commissioner Christopher Cook to serve as interim head of the parks system. Cook is a highly regarded administrator at City Hall. But he has no prior experience managing a park system.

If Cook wants to make a case for the permanent job, he’d be smart to focus on the Common. A good start might be to shift some of the turf-pounding events on the Common to the brick plaza at City Hall. Cook, who used to be in charge of special events during the prior Menino administration, knows a lot about finding sites. Other bold moves could be considered, such as introducing artificial turf in some of the more heavily used sections of the Common, such as the Parade Ground near Charles and Beacon streets. Even America’s first and oldest park, established in 1634, might benefit from some synthetic fiber.

What is needed most, according to the Friends of the Public Garden, is a park superintendent whose sole responsibility would be to oversee and protect the Common, especially during the busy schedule of events. A dedicated supervisor could also address ongoing problems such as careless or overzealous work crews who “scalp” the grass, bang up benches with snow plows, and scar the grounds while driving through to pick up trash.

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The Common isn’t meant to mirror the museum-like quality of the Public Garden. Heavy use belongs on the Common. But it can quickly cross over into abuse. Great cities manage to create signature downtown parks that are both vibrant and well-kept. There is no justifiable reason why Boston should be the scrubby exception.